Several times, House is actually holding the very weakened perpetrator's right arm (which is holding the gun) as he administers shots, but never once simply bends it backwards to disarm the man. During those times, the gun is pointed at the floor, so no one was in immediate danger.
When House puts the perpetrator in the MRI machine, he stops at his head. He should have put his whole body in, so when the MRI was turned on, the gun would be pulled to the wall of the MRI by the magnetic field violently and likely out of the guy's hand.
The goof item below may give away important plot points.
Just as the wall is blown in by the SWAT team to end the hostage situation, Jason's (the hostage taker) face is covered in white make-up, so the character is covered in dust before the explosion debris has reached him.